An alloy of Cd and Bi contains 25% of Cd. Find the mass of eutectic in 1 kg of the solid alloy, if the eutectic contains 40% of Cd. (asked in MU June 2025 KT; also Dec 2025)

Answer: Mass of eutectic \(=625\) g; the remaining 375 g is pure Bi.

The alloy (25% Cd) has less Cd than the eutectic (40% Cd), so it lies on the Bi-rich side of the eutectic point. On cooling, pure Bi crystallises first until the liquid reaches the eutectic composition; the remaining liquid then solidifies as eutectic. All the Cd therefore ends up in the eutectic.

Mass of Cd in 1 kg alloy \(=\dfrac{25}{100}\times1000=250\) g.

If the mass of eutectic is \(x\) g, it contains 40% Cd:

\[\frac{40}{100}\,x=250\ \Rightarrow\ x=\frac{250\times100}{40}=625\ \text{g}\]

Mass of pure Bi that separates out \(=1000-625=375\) g.

Check: Bi in eutectic \(=0.60\times625=375\) g; total Bi \(=375+375=750\) g \(=75\%\) of 1 kg. ✓